Small 3-manifolds of large genus

2002/05/09 by Ian Agol, Agol, Ian · 2 citations
Mathematics · #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0205091

10 pages, 12 figures

arxiv created 2002/05/09 · arxiv updated 2009/11/30

Abstract

We prove the existence of pure braids with arbitrarily many strands which are small, i.e. they contain no closed incompressible surface in the complement which is not boundary parallel. This implies the existence of irreducible non-Haken 3-manifolds of arbitrarily high Heegaard genus.

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